A simplex-simplex approach for mixed aleatory-epistemic uncertainty quantification

The Simplex Stochastic Collocation (SSC) method has been recently proposed in order to handle aleatory uncertainty quantification (UQ), i.e. irreducible variabilities inherent in nature. In this work, we present an extension of this method for treating epistemic uncertainty in the context of interval analysis approach. This numerical method is based on a Simplex space representation, high-order polynomial interpolation and adaptive refinements, permitting to treat mixed aleatory-epistemic uncertainties. This method displays good properties in terms of accuracy and computational cost. Several numerical examples are presented to demonstrate the properties of the proposed method.